3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{124ee19f-8a49-42df-9f4b-5a1cc2139be9-06_725_668_118_639}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation \(y = \log _ { 10 } x\)
The region \(R\), shown shaded in Figure 1, is bounded by the curve, the line with equation \(x = 2\), the \(x\)-axis and the line with equation \(x = 14\)
Using the trapezium rule with four strips of equal width,
- show that the area of \(R\) is approximately 10.10
- Explain how the trapezium rule could be used to obtain a more accurate estimate for the area of \(R\).
- Using the answer to part (a) and making your method clear, estimate the value of
- \(\quad \int _ { 2 } ^ { 14 } \log _ { 10 } \sqrt { x } \mathrm {~d} x\)
- \(\int _ { 2 } ^ { 14 } \log _ { 10 } 100 x ^ { 3 } \mathrm {~d} x\)